Homework is given to a child who is not ready for a math competition - (3).

So my teacher gave me this homework, and I am stuck:

$a$, $b$ and $c$ are three positives such that $abc \le 1$. Calculate the minimum value of

$\large \displaystyle \sqrt{\dfrac{a^2 + b}{bc + c + 1}} + \sqrt{\dfrac{b^2 + c}{ca + a + 1}} + \sqrt{\dfrac{c^2 + a}{ab + b + 1}}$

If you can help me, not with a full solution, but the first step to solving the problem, then feel free to write in the comments' section.

Notation: I haven't studied advanced calculus yet, so please give me a clue in pure algebra.

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$